20140529

Physics final exam question: manipulating Feynman diagram paths

This (valid) Feynman diagram depicts electron capture. Demonstrate how the paths on this diagram can be manipulated to depict β+ decay. (Ignore the direction of the interaction particle, but all other particle paths must have the correct directions and labels.) Explain your reasoning using the properties of Feynman diagrams, particles and antiparticles, and interactions.

Solution and grading rubric:

p:Correct. Demonstrates how left-to-right path of electron entering
the vertex can be draw exiting the vertex, but with a right-to-left arrow
direction, representing a positron (a "β+" particle) as a decay particle,
along with a neutrino, as a proton converts into a neutron.

r:As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Error in keeping direction of electron/positron path consistent as it is
flipped, making the vertex invalid, but understands that beta-plus decay process
has only proton decaying into byproducts (as opposed to a proton-to-neutron
conversion by antineutrino bombardment).

t:Nearly correct, but argument has conceptual errors, or is incomplete. At least some attempt at showing a positron-out process, despite drawing invalid
Feynman diagrams and/or neutrino/antineutrino bombardment of a nucleon by
path/direction manipulation of given electron capture Feynman diagram.

v:Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some use of Feynman diagrams
or some other attempt, but no positron output.

x:Implementation/application of ideas, but credit given for effort rather than merit.

A sample "r" response (from student 7810), with an invalid vertex due to the wrong electron path direction:

A sample "t" response (from student 6644), at least showing a valid Feynman diagram with an exiting positron path, but with an incoming antineutrino path, and a strange antineutron-to-antiproton conversion: